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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
981.1.d.a	$981$	$1$	981.d	327.d	$2$	$2$	$2$	$0.490$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}-\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\beta q^{13}+\cdots$
981.1.d.b	$981$	$1$	981.d	327.d	$2$	$2$	$2$	$0.490$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$2$	$0$	$0$	$2$		$1$		$q+q^{2}-\beta q^{5}+q^{7}-q^{8}-\beta q^{10}-\beta q^{13}+\cdots$
981.1.j.a	$981$	$1$	981.j	109.d	$4$	$2$	$1$	$0.490$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-iq^{4}+q^{7}+(-1+i)q^{13}-q^{16}+\cdots$
981.1.l.a	$981$	$1$	981.l	327.i	$6$	$4$	$2$	$0.490$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta _{3}q^{2}-q^{4}+\beta _{2}q^{7}+\beta _{1}q^{11}+(\beta _{1}+\cdots)q^{14}+\cdots$
981.1.n.a	$981$	$1$	981.n	981.n	$6$	$2$	$1$	$0.490$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{109}) $		$4$	$0$	$0$	$1$	$3$	$-2$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
981.1.z.a	$981$	$1$	981.z	109.g	$12$	$4$	$1$	$0.490$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{3}q^{4}+\zeta_{12}^{2}q^{7}+(\zeta_{12}^{2}+\zeta_{12}^{5}+\cdots)q^{13}+\cdots$
981.1.bc.a	$981$	$1$	981.bc	981.ac	$12$	$4$	$1$	$0.490$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$2$	$2$	$2$	$0$		$1$		$q+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}q^{4}+\cdots$
981.1.bx.a	$981$	$1$	981.bx	109.j	$36$	$12$	$1$	$0.490$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+\zeta_{36}^{15}q^{4}+(-\zeta_{36}^{6}-\zeta_{36}^{14})q^{7}+\cdots$
981.2.a.a	$981$	$2$	981.a	1.a	$1$	$1$	$1$	$7.833$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{5}+2q^{7}+3q^{8}+3q^{10}+\cdots$
981.2.a.b	$981$	$2$	981.a	1.a	$1$	$1$	$1$	$7.833$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
981.2.a.c	$981$	$2$	981.a	1.a	$1$	$3$	$3$	$7.833$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$6$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(3+\cdots)q^{5}+\cdots$
981.2.a.d	$981$	$2$	981.a	1.a	$1$	$3$	$3$	$7.833$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
981.2.a.e	$981$	$2$	981.a	1.a	$1$	$4$	$4$	$7.833$	4.4.7537.1	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots$
981.2.a.f	$981$	$2$	981.a	1.a	$1$	$6$	$6$	$7.833$	6.6.16371248.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$0$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
981.2.a.g	$981$	$2$	981.a	1.a	$1$	$6$	$6$	$7.833$	6.6.3356224.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots$
981.2.a.h	$981$	$2$	981.a	1.a	$1$	$9$	$9$	$7.833$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-3$	$0$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(1+\beta _{5}+\cdots)q^{7}+\cdots$
981.2.a.i	$981$	$2$	981.a	1.a	$1$	$12$	$12$	$7.833$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{11}q^{5}+(1+\cdots)q^{7}+\cdots$
981.2.c.a	$981$	$2$	981.c	109.b	$2$	$2$	$2$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}+3q^{5}+2q^{7}-\zeta_{6}q^{8}+\cdots$
981.2.c.b	$981$	$2$	981.c	109.b	$2$	$4$	$4$	$7.833$	4.0.27648.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-12$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-3q^{5}+(2+\cdots)q^{7}+\cdots$
981.2.c.c	$981$	$2$	981.c	109.b	$2$	$6$	$6$	$7.833$	6.0.191244096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$-10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
981.2.c.d	$981$	$2$	981.c	109.b	$2$	$6$	$6$	$7.833$	6.0.49843600.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+2q^{5}-\beta _{3}q^{7}+\cdots$
981.2.c.e	$981$	$2$	981.c	109.b	$2$	$8$	$8$	$7.833$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{5}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
981.2.c.f	$981$	$2$	981.c	109.b	$2$	$8$	$8$	$7.833$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{4}q^{4}-\beta _{2}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
981.2.c.g	$981$	$2$	981.c	109.b	$2$	$12$	$12$	$7.833$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-327}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{7}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
981.2.e.a	$981$	$2$	981.e	9.c	$3$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-1$	$-3$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
981.2.e.b	$981$	$2$	981.e	9.c	$3$	$106$	$53$	$7.833$		$_{}$	None	None		$2$	$0$	$-5$	$1$	$-14$	$4$			$\mathrm{SU}(2)[C_{3}]$
981.2.e.c	$981$	$2$	981.e	9.c	$3$	$108$	$54$	$7.833$		$_{}$	None	None		$2$	$0$	$4$	$-2$	$17$	$0$			$\mathrm{SU}(2)[C_{3}]$
981.2.f.a	$981$	$2$	981.f	981.f	$3$	$216$	$108$	$7.833$		$_{}$	None	None		$2$	$0$	$-2$	$-1$	$5$	$0$			$\mathrm{SU}(2)[C_{3}]$
981.2.g.a	$981$	$2$	981.g	981.g	$3$	$216$	$108$	$7.833$		$_{}$	None	None		$2$	$0$	$-2$	$-1$	$-10$	$0$			$\mathrm{SU}(2)[C_{3}]$
981.2.h.a	$981$	$2$	981.h	109.c	$3$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-q^{4}+(1-\zeta_{6})q^{7}+3q^{8}-2\zeta_{6}q^{11}+\cdots$
981.2.h.b	$981$	$2$	981.h	109.c	$3$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-q^{4}+(1-\zeta_{6})q^{7}-3q^{8}+2\zeta_{6}q^{11}+\cdots$
981.2.h.c	$981$	$2$	981.h	109.c	$3$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-q^{4}+(2-2\zeta_{6})q^{5}+(-4+4\zeta_{6})q^{7}+\cdots$
981.2.h.d	$981$	$2$	981.h	109.c	$3$	$14$	$7$	$7.833$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$0$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(\beta _{4}-\beta _{6})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
981.2.h.e	$981$	$2$	981.h	109.c	$3$	$18$	$9$	$7.833$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}-\beta _{13}q^{5}+\beta _{8}q^{7}+\cdots$
981.2.h.f	$981$	$2$	981.h	109.c	$3$	$20$	$10$	$7.833$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$4$		$5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{2})q^{4}+(-\beta _{14}+\cdots)q^{5}+\cdots$
981.2.h.g	$981$	$2$	981.h	109.c	$3$	$32$	$16$	$7.833$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{3}]$
981.2.i.a	$981$	$2$	981.i	327.f	$4$	$76$	$38$	$7.833$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{4}]$
981.2.k.a	$981$	$2$	981.k	109.e	$6$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}-q^{4}+(1-\zeta_{6})q^{7}+\cdots$
981.2.k.b	$981$	$2$	981.k	109.e	$6$	$2$	$1$	$7.833$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}-q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
981.2.k.c	$981$	$2$	981.k	109.e	$6$	$14$	$7$	$7.833$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(\beta _{1}+2\beta _{2}-\beta _{5}+\beta _{11}-\beta _{12}+\cdots)q^{4}+\cdots$
981.2.k.d	$981$	$2$	981.k	109.e	$6$	$16$	$8$	$7.833$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{3}-\beta _{4})q^{2}+(-1+\beta _{1})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
981.2.k.e	$981$	$2$	981.k	109.e	$6$	$18$	$9$	$7.833$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{5})q^{2}+(-1+\beta _{1})q^{4}+\beta _{12}q^{5}+\cdots$
981.2.k.f	$981$	$2$	981.k	109.e	$6$	$40$	$20$	$7.833$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
981.2.q.a	$981$	$2$	981.q	981.q	$6$	$216$	$108$	$7.833$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
981.2.r.a	$981$	$2$	981.r	981.r	$6$	$216$	$108$	$7.833$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$0$			$\mathrm{SU}(2)[C_{6}]$
981.2.u.a	$981$	$2$	981.u	981.u	$6$	$216$	$108$	$7.833$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
981.2.w.a	$981$	$2$	981.w	109.f	$9$	$42$	$7$	$7.833$		$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$3$			$\mathrm{SU}(2)[C_{9}]$
981.2.w.b	$981$	$2$	981.w	109.f	$9$	$54$	$9$	$7.833$		$_{}$	None	None		$2$	$0$	$3$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
981.2.w.c	$981$	$2$	981.w	109.f	$9$	$66$	$11$	$7.833$		$_{}$	None	None		$2$	$0$	$3$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{9}]$
981.2.w.d	$981$	$2$	981.w	109.f	$9$	$108$	$18$	$7.833$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{9}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.